Optimal and Suboptimal Control of a Standard Brownian Motion

Optimal and Suboptimal Structure From Motion

\Structure From Motion" (SFM) refers to the problem of estimating three-dimensional information about the environment from the motion of its two-dimensional projection onto a surface (for instance the retina). Noise plays an important role in this problem, but it has been addressed only marginally in more than twenty years of research. We present an analysis of SFM from the point of view of noi...

Impulse Control of Brownian Motion

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON–OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizondiscounted cost, and thefinite-horizon cost. In addition, wefind a solution to a constrained minimization problem as an applicati...

Optimal control of a stochastic network driven by a fractional Brownian motion input

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite horizon discounted cost, and the finite horizon cost. In addition, we find a solution to a constrained minimization problem as an applic...